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put this solution on YOUR website!A tedious looking problem which is no doubt created to torment young minds, however, on closer inspection we can see that it can be unravelled without too much difficulty.
:
Get each equation in the ax + by + cz = d format:
Eq1:
32 + 3z = 4(x-2y)
32 + 3z = 4x - 8y
-4x + 8y + 3z = -32
:
Eq2:
4(x-2y-z) = -36
4x - 8y - 4z = -36
:
:
Eq3:
-2(2x+y) + 2z = -12
-4x - 2y + 2z = -12
:
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Let's just deal with the 1st two equations; notice if we add them we will eliminate x and y, leaving us with the solution to z:
:
-4x + 8y + 3z = -32
4x - 8y - 4z = - 36
-------------------- add
0x + 0y - 1z = -68
z = -68/-1
z = +68
:
Take eq 2 & 3, substitute 68 for z giving us two equations with two unknowns:
Eq2: 4x - 8y - 4z = -36 > > 4x - 8y - 4(68) = -36 > > 4x - 8y - 272 = -36
Eq3 -4x - 2y + 2z = -12 > > -4x - 2y + 2(68) = -12 > > -4x -2y + 136 = -12
:
Combining the numbers:
4x - 8y = -36 + 272
-4x -2y = -12 - 136
:
We have two managable equations, adding them eliminates x, giving the y solution
4x - 8y = + 236
-4x - 2y = - 148
---------------- add
0x - 10y = + 88
y = +88/-10
y = - 8.8
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Now we have y = -8.8 and z = + 68, almost done, let's substitute for y & z in the 3rd equation
-4x - 2y + 2z = -12
-4x - 2(-8.8) + 2(68) = -12
:
-4x + 17.6 + 136 = -12
-4x = -12 - 17.6 - 136
-4x = -165.6
x = -165.6/-4
x = +41.4
:
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